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Title Name Amity Solved Assignment BSC for Computer Oriented Numerical Analysis
University AMITY
Service Type Assignment
Course B.Sc-(IT)
Semester Semester-II Course: B.Sc-(IT)
Session
Short Name or Subject Code Computer Oriented Numerical Analysis
Commerce line item Type Semester-II Course: B.Sc-(IT)
Product Assignment of B.Sc-(IT) Semester-II (AMITY)
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Questions:-


COURSE: BSC (IT)

SUBJECT:  COMPUTER ORIENTED NUMERICAL ANALYSIS

 

 

ASSIGN MENT-A

(Any three)

  1. Solve the following set of equation by Gauss elimination method.

               2x +3y+4z=12

               3x + y +z=4

               x+4y+z=5

SOLUTION

          

  1. Find the rate of convergence of Newton Raphson method. Solve by www.solvezone.in

 Solution

  1. Define error, relative error and absolute error, give example of each.

Solution

ASSIGNMENT-B

  1. a) Round off and truncate the following numbers to the four decimal places.
  2. a) 132.5983  
  1. b) 0.073729

 

Solution -   

  1. Solve the following equation by Jacobi method. Perform three steps.

 x₁-2x₂-x₃-x₄=3

-2x₁ + x₂-x₃ -x₄=15

x₁ – x₂ + x₃ -2x₄ =27

-x₁ -x₂-2x₃+x₄ =-9

Solution

  1. For a given data

X

F(x)

1

33

2

50

3

69

4

90

5

129

Find the value of f(x) at 1.4

Solution

ASSIGNMENT C

 

 

  1. The order of convergence of Newton-Raphson method is

 (A): 2

 (B): 3

 (C): 0

 (D): 1

  1. One of the roots of the equation x3-3x2+x-3=0 is

 (A): -1

 (B): 1

 (C): √3

 (D): 3

  1. The solution to the set of equations:

25x+y+z=25; 64x+8y+z=71; 114x+12y+z=155

The most nearly value of ??,??,??=

 (A): (1,1,1)

 (B):  (1,-1,1)

 (C):  (1,1,-1)

 (D):  Does not have a unique solution

  1. The order of convergence of Regula-falsi method is

 (A): 1.235

 (B): 3.141

 (C): 1.618

 (D): 2.792

  1. Newton’s iterative formula to find the value of √N is

Ans. D

  1. The Newton-Raphson method fails when

Ans. D

  1. The one of the root of the equation x^3-4x-9=0 using bisection method is

 (A): 2.5065

 (B): 2.6066

 (C): 2.7066

 (D): 3.5066

  1. Which of the following is increasing order of convergence method for finding roots

 (A):  Bisection, regula-falsi, newton Raphson

 (B): Regula-falsi, Bisection, Newton Raphson

 (C): Newton Raphson, Regula falsi, bisection

 (D): Bisection, Newton Raphson, regula-falsi

  1. If X is a true value and X is its approximate value then absolute error ea is

Ans- A

  1. If X is a true value and X is its approximate value then Relative error er is

Ans. D

  1. Any quadratic equation f(x)=0 has

 (A): One root

 (B): Two roots

 (C): Three roots

 (D): Four roots

  1. An equation such as tanx=x has

 (A): Zero roots

 (B): One root

 (C): Two roots

 (D): Infinite roots

  1. The roots of an equation f(x)=x^3-x-1=0 lies between

 (A): f(2)  and f(3)

 (B): f(3)  and f(4)

 (C): f(1)  and f(2)

 (D): All of these

  1. The real roots of an equation f(x)=xex-2=0 using newton Raphson method is

 (A): 0.5682

 (B): 0.8526

 (C): 0.3525

 (D): 1.5000

  1. Given n+1 data pairs (x_0,y_0),(x_1,y_1),… (x_n,y_n). The process of finding the value of y corresponding to any value of x (between x_0 and x_n) is called

 (A): Extrapolation

 (B): Interpolation

 (C): Differentiation

 (D): Integration

  1. Given n+1 data pairs (x_0,y_0),(x_1,y_1),… (x_n,y_n). The process of finding the value of y corresponding to any value of x (outside of the range x_0 and x_n) is called

 (A): Extrapolation

 (B): Interpolation

 (C): Differentiation

 (D): Integration

  1. Given n+1 data pairs (x_0,y_0),(x_1,y_1),… (x_n,y_n). The n^(th ) forward difference is

 (A): ?n yr=?(n-1) y(r+1)-?(n-1) yr

 (B): ?n yr=?(n-1) y(r+1)-?(n-1) yr

 (C): ?^n y_r=?^n y_(r+1)-?^n y_r

 (D): ?^n y_r=?^n y_r-?^(n-1) y_(r-1)

  1. If ? is forward difference operator and E is a shift operator then

 (A): ?=E-1

 (B): ?=E+1

 (C): E=?-1

 (D): None of these

  1. If δ is central difference operator and E is a shift operator then

Ans. D

  1. The rate of convergence of Bisection method for finding roots is

 (A): 2

 (B): 3

 (C): 1.5

 (D): 1.0

  1. A second degree polynomial passes through (0,1),(1,3), (2,7), (3,13), then the polynomial f(x) is

Ans- C

  1. Given data pairs (1,7),(2,x),(3,13),(4,21),(5,37). The value of x is

 (A): 10.5

 (B): 9.5

 (C): 12.5

 (D): 12.0

  1. Which of the following Interpolation formula is used for unequally spaced points

 (A): Newton forward

 (B): Newton backward

 (C): Lagrange formula

 (D): Euler formula

  1. 1)=1, P(3)=27, P(4)=64, Using Lagrange interpolation formula, the polynomial P(x) of degree 2 is:

Ans. D

  1. Putting n=1 in the newton-Cote’s quadrature formula, we have

 (A): Trapezoidal rule

 (B): Simpson’s 1/3 formula

 (C): Simpson’s 3/8 formula

 (D): Euler’s formula

  1. Putting n=3 in the newton-Cote’s quadrature formula, we have

 (A): Trapezoidal rule

 (B): Simpson’s 1/3 formula

 (C): Simpson’s 3/8 formula

 (D): Euler’s formula

  1. Which of the following method required odd number of points for integration

 (A): Trapezoidal rule

 (B): Simpson’s  formula

 (C): Both Trapezoidal & Simpson

 (D): None of these

  1. Using Trapezoidal rule, the value of

 (A): 1.3662

 (B): 1.4107

 (C): 1.3570

 (D): 1.5706

  1. Which of the following symbol is called backward difference operator

 (A): ?

 (B):

 (C): δ

 (D): E

  1. Newton divided difference method for interpolation can be used for

 (A):  Equal spaced points

 (B): Unequal spaced points

 (C): Not well defined

 (D): All of these

  1. Which of the following is NOT a method to solve ordinary differential equation

 (A): Euler’s method

 (B): Picard’s method

 (C): Taylor series method

 (D): Romberg’s method

  1. Euler’s formula for solving ordinary differential equation is

Ans. D

  1. Which of the following is a Runga kutta 2nd order formula

Ans. C

  1. Taylor series method is used for

 (A): Integration

 (B): Differentiation

 (C): Ordinary differential equation

 (D): Roots finding

  1. Polynomials are most commonly used functions for interpolation because they are easy to

 (A): Evaluate

 (B): Differentiate

 (C): Integrate

 (D): Evaluate, differentiate, and integrate

  1. To solve the ordinary differential equation using Runga kutta 2nd order, we need to write the equation

Ans. D

  1. Picard’s method is used to solve

 (A): Integration

 (B): Differentiation

 (C): Ordinary Differential equation

 (D): Roots finding

  1. The inverse of a matrix A is written as

     

 (A): Identity matrix

 (B): Null matrix

 (C): Singular matrix

 (D): Inverse matrix

  1. he second forward difference
  2.  

Ans. D


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